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## Henry Bushby Transcription pages

### VM533B94v4-p139.jpg

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139__ General Principles. __

(1) A r.k. is a knot expressed in

one of the figures of which ^ * the * charac-

ter is shown in vol ii. __ ad fin. __

(2) Every complication can be expressed

as a r.k. but in this form it

may or may not show its least

no. of crossings.

(3) Every group (G) of ^ * r. * knots ~~ such ~~ ^ * e.g. *~~ as ~~ Plaits (P) ~~ or ~~ ^ * and * Torsions (K) has

alternate equal sequences of crossings

over & under.

(4) The sequence defines the group

& must be a (& may be any) measure

of (n - 1) from n - (n - 1) [=1] to

n - 1. Thus the seq. in P is 1 or

n - (n - 1); in K it is (n - 1). These

two groups represent the two ex-

tremes. Between them lie :-